DEDUCTIVE REASONING. 63 



the ancient Greek ^aX/co? is our copper, then it must be 

 the French cuivre, the German kupfer, the Latin cuprum, 

 because -these are words, in one sense at least, equivalent 

 to copper. Whenever we can give two definitions or 

 expressions for the same term, the formula applies ; thus 

 Senior defined wealth as ' whatever is transferable, limited 

 in supply, and productive of pleasure or preventive of 

 pain ;' it is also equivalent to ' whatever has value in 

 exchange ;' hence obviously ' Whatever has value in ex- 

 change' = * Whatever is transferable, limited in supply, and 

 productive of pleasure or preventive of pain/ Two ex- 

 pressions for the same term are often given in the same 

 sentence, and their equivalency implied. Thus Thomson 

 and Tait say c , ' The naturalist may be content to know 

 matter as that which can be perceived by the senses, or as 

 that which can be acted upon by or can exert force.' I 

 take this to mean 



Matter = what can be perceived by the senses ; 



Matter =-. what can be acted upon by or can exert force. 

 For the term ' matter' in either of these identities we 

 may substitute its equivalent given in the other definition. 

 Elsewhere they often employ sentences of the form exem- 

 plified* in the folio wing d ; ' The integral curvature, or whole 

 change of direction of an arc of a plane curve, is the angle 

 through which the tangent has turned as we pass from 

 one extremity to the other/ This sentence is certainly of 

 the form 



The integral curvature = the whole change of direction, 

 &c. = the angle through which the tangent has 

 turned, &c. 



Disguised cases of the same kind of inference occur 

 throughout all sciences, and a remarkable instance is 

 found in algebraic geometry. Mathematicians readily 



c 'Treatise on Natural Philosophy,' vol. i. p. 161. 

 41 Ibid. vol. i. p. 6. 



